1 Chapter 10: Key Management in Public key cryptosystems Fourth Edition by William Stallings Lecture slides by Lawrie Brown (Modified by Prof. M. Singhal, U of Kentucky)

2 Key Management public-key encryption helps address key distribution problems have two aspects of this: –distribution of public keys –use of public-key encryption to distribute secret keys

3 Distribution of Public Keys can be considered as using one of: –public announcement –publicly available directory –public-key authority –public-key certificates

4 Public Announcement users distribute public keys to recipients or broadcast to community at large –E.g., append PGP keys to messages or post to news groups or list major weakness is forgery –anyone can create a key claiming to be someone else and broadcast it –until forgery is discovered can masquerade as claimed user

5 Publicly Available Directory can obtain greater security by registering keys with a public directory directory must be trusted with properties: –contains {name,public-key} entries –participants register securely with directory –participants can replace key at any time –directory is periodically published –directory can be accessed electronically still vulnerable to tampering or forgery

6 Public-Key Authority improve security by tightening control over distribution of keys from directory has properties of directory and requires users to know public key for the directory then users interact with directory to obtain any desired public key securely –does require real-time access to directory when keys are needed

7 Public-Key Authority

8 Public-Key Certificates certificates allow key exchange without real-time access to public-key authority a certificate binds identity to public key -contains other info such as period of validity, rights of use, etc. with all contents signed by a trusted Public-Key or Certificate Authority (CA) can be verified by anyone who knows the public-key authorities public-key

9 Public-Key Certificates

10 Public-Key Distribution of Secret Keys use previous methods to obtain public-key can use for secrecy or authentication but public-key algorithms are slow so usually want to use private-key encryption to protect message contents hence need a session key have several alternatives for negotiating a suitable session key

11 Simple Secret Key Distribution proposed by Merkle in 1979 –A generates a new temporary public key pair –A sends the public key and its identity to B –B generates a session key K and sends it to A encrypted using the supplied public key –A decrypts the session key and both use problem is that an opponent can intercept and impersonate both halves of protocol

12 Public-Key Distribution of Secret Keys A & B have securely exchanged public- keys: -Insures both (i) confidentiality and (ii) authentication.

13 Hybrid Key Distribution retain use of private-key KDC shares secret master key with each user distributes session key using master key public-key used to distribute master keys –Three-level hierarchy. rationale –Performance (public key cryptography is used the least frequently.)

14 Diffie-Hellman Key Exchange by Diffie & Hellman in 1976 along with the exposition of public key concepts –Williamson secretly proposed the concept in 1970 is a practical method for public exchange of a secret key --even when two parties do not know each other (they share no secret information). -does not require a third party (like KDC).

15 Diffie-Hellman Key Exchange a public-key distribution scheme –cannot be used to exchange an arbitrary message –rather it can establish a common key –known only to the two participants value of key depends on the participants (and their private and public key information) based on exponentiation in a finite (Galois) field (modulo a prime or a polynomial) security relies on the difficulty of computing discrete logarithms (similar to factoring) – hard

16 Diffie-Hellman Setup all users agree on global parameters: –large prime integer or polynomial q –number a that is a primitive root mod q each user (e.g., A) does the following: -chooses a secret key (number): x A < q -computes: y A = a x A mod q -sends y A to the other party.

17 Diffie-Hellman Key Exchange shared session key for users A & B is K AB : K AB = a x A. x B mod q = y A x B mod q (which B can compute) = y B x A mod q (which A can compute) K AB is used as session key in private-key encryption scheme between Alice and Bob attacker needs an x, must solve discrete log

18 Diffie-Hellman Example users Alice & Bob who wish to swap keys: agree on prime q=353 and a=3 select random secret keys: –A chooses x A =97, B chooses x B =233 compute respective public keys: –y A = 3 97 mod 353 = 40 (Alice) –y B = mod 353 = 248 (Bob) compute shared session key as: –K AB = y B x A mod 353 = = 160 (Alice) –K AB = y A x B mod 353 = = 160 (Bob)

19 Key Exchange Protocols vulnerable to a meet-in-the-Middle Attack authentication of the keys is needed

20 Summary have considered: –distribution of public keys –public-key distribution of secret keys –Diffie-Hellman key exchange